MIT6_003S10_assn13

# MIT6_003S10_assn13 - 6.003 Homework 13 Please do the...

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6.003 Homework 13 Please do the following problems by Wednesday, May 12, 2010 . your answers: they will NOT be graded. Solutions will be posted. You need not submit Problems 1. Transformation Consider the following transformation from x ( t ) to y ( t ) : × × × + x ( t ) y ( t ) p ( t ) cos( πt ) w 1 ( t ) w 2 ( t ) w 3 ( t ) where p ( t ) = k = −∞ δ ( t k ) . Determine an expression for y ( t ) when x ( t ) = sin( πt/ 2) / ( πt ) . 2. DT processing of CT signals Consider the following system for DT processing of CT signals: H 1 ( ) H 2 ( e j ) H 3 ( ) uniform sampler sample-to- impulse x a ( t ) x b ( t ) x c [ n ] y d [ n ] y e ( t ) y f ( t ) where x c [ n ] = x b ( nT ) and y e ( t ) = y d [ n ] δ ( t nT ) . n = −∞ The frequency responses H 1 ( ) and H 3 ( ) are given below. ω π 2 T π 2 T 3 π 2 T 3 π 2 T H 1 ( ) 1 ω π T π T H 3 ( ) T Part a. Assume in this part that H 2 ( e j ) = 1 for all frequencies . Determine y f ( t ) when π 5 π x a ( t ) = cos t + sin t . 2 T 4 T Part b. For this part, assume that H 2 ( e j ) = 1 ; | | < c 0 ; c < | | < π .

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